In the laboratory, partially water-wet systems are often mistaken for completely oil-wet systems, because imbibition only starts after removal of the oil layer, which originally covers the grains. The (long) time required to remove the oil film will be referred to as delay time. Incorporation of delay time in a more general description of capillary pressure and relative permeability functions is called the non-equilibrium effect. No attempt has yet been made to model non-equilibrium effects in fractured reservoirs for a field-scale problem and this is the main innovative aspect of this paper. We apply homogenization to derive an upscaled model for fractured reservoirs and include delay time effects. Furthermore, we develop a computationally efficient numerical approach to solve the upscaled model. The upscaled model overcomes limitations of the dual-porosity model including the use of a transfer function and shape factor. This paper examines various aspects of wettability behavior in fractured reservoirs, viz., the contact angle, mixed wetting, and non-equilibrium effects in capillary pressure. The main characteristic that determines reservoir behavior is the Peclet number that expresses the ratio of the average imbibition time divided by the residence time of the fluids in the fractures.

At low Peclet numbers and thus high gravity numbers, under-riding is aggravated by large contact angles and longer delay times. However, for low Peclet and low gravity numbers, the effect of contact angle and delay time for the non-equilibrium effects can be ignored without appreciable loss of accuracy. For low Peclet numbers, the recovery for the mixed-wet fracture/mixed-wet matrix case is more than for the water-wet fracture/mixed-wet matrix case because a combination of capillary imbibition and gravity drainage occurs in the former case. For low Peclet numbers, the ultimate oil recovery for the water-wet fracture/mixed-wet matrix case is about the matrix Amott index times the recovery obtained for completely water-wet reservoirs. For residence times of water in the fractured reservoir much longer than the delay time, the delay time (non-equilibrium effect) does not influence the oil recovery qualitatively. Conversely, for high Peclet numbers, the residence time of water in the fractures is short and the relatively longer delay times reduce the cumulative oil production considerably as expected. Furthermore, at high Peclet numbers, after water breakthrough, the oil recovery appears to be approximately proportional to the cosine of the contact angle. It is important to distinguish between truly oil-wet systems and systems that are water-wet with long delay times. The efficiency of waterflooding in naturally fractured oil reservoirs decreases in the sequence of completely water-wet, mixed-wet fracture/mixed-wet matrix, water-wet fracture/mixed-wet matrix, and completely oil-wet, respectively. For the same amount of injected water, the recovery at low Peclet numbers is larger than the recovery at high Peclet numbers.

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